Quantitative analysis of microscopy images is increasingly important in clinical researchers' efforts to unravel the cellular and molecular determinants of disease, and for pathological analysis of tissue samples. Yet, manual segmentation and measurement of cells or other features in images remains the norm in many fields. We report on a new system that aims for robust and accurate semi-automated analysis of microscope images. A user interactively outlines one or more examples of a target object in a training image. We then learn a cost function for detecting more objects of the same type, either in the same or different images. The cost function is incorporated into an active contour model, which can efficiently determine optimal boundaries by dynamic programming. We validate our approach and compare it to some standard alternatives on three different types of microscopic images: light microscopy of blood cells, light microscopy of muscle tissue sections, and electron microscopy cross-sections of axons and their myelin sheaths.